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Let's address each question step by step.

**1. Xác định giá và sản lượng cân bằng? Tính CS và PS tại mức giá cân bằng?**

Given the demand and supply equations:
\[ P_D = 65 - 0.5Q \]
\[ P_S = 15 + 0.5Q \]

At equilibrium, \( P_D = P_S \). So we set the equations equal to each other to find the equilibrium quantity \( Q \):
\[ 65 - 0.5Q = 15 + 0.5Q \]

Solving for \( Q \):
\[ 65 - 15 = 0.5Q + 0.5Q \]
\[ 50 = Q \]

Now, substitute \( Q = 50 \) back into either the demand or supply equation to find the equilibrium price \( P \):
\[ P = 65 - 0.5(50) \]
\[ P = 65 - 25 \]
\[ P = 40 \]

Equilibrium price \( P = 40 \) and equilibrium quantity \( Q = 50 \).

Consumer Surplus (CS) is the area above the price level and below the demand curve:
\[ CS = \frac{1}{2} \times (65 - 40) \times 50 = \frac{1}{2} \times 25 \times 50 = 625 \]

Producer Surplus (PS) is the area below the price level and above the supply curve:
\[ PS = \frac{1}{2} \times (40 - 15) \times 50 = \frac{1}{2} \times 25 \times 50 = 625 \]

**2. Khi chính phủ đặt P = 30 thì điều gì xảy ra? Tính CS tại mức giá đó?**

Given \( P = 30 \):
\[ 30 = 65 - 0.5Q \]
\[ 0.5Q = 35 \]
\[ Q = 70 \]

Price \( P = 30 \) results in quantity \( Q = 70 \).

New Consumer Surplus:
\[ CS = \frac{1}{2} \times (65 - 30) \times 70 = \frac{1}{2} \times 35 \times 70 = 1225 \]

**3. Giả sử chính phủ đánh thuế t = 10/SP thì giá và sản lượng cân bằng mới thế nào?**

The new supply equation with tax \( t = 10 \) per unit:
\[ P_S' = 15 + 0.5Q + 10 \]
\[ P_S' = 25 + 0.5Q \]

Set the new supply equation equal to the demand equation:
\[ 65 - 0.5Q = 25 + 0.5Q \]
\[ 65 - 25 = Q \]
\[ 40 = Q \]

Substitute \( Q = 40 \) back into the new supply equation:
\[ P = 25 + 0.5(40) = 25 + 20 = 45 \]

New equilibrium price \( P = 45 \) and new equilibrium quantity \( Q = 40 \).

**4. Giả sử nhờ quảng cáo làm lượng cầu tại mỗi mức giá tăng 30 đơn vị, xác định cân bằng mới?**

New demand equation with an increase of 30 units:
\[ P_D' = 65 - 0.5(Q - 30) \]
\[ P_D' = 65 - 0.5Q + 15 \]
\[ P_D' = 80 - 0.5Q \]

Set the new demand equation equal to the original supply equation:
\[ 80 - 0.5Q = 15 + 0.5Q \]
\[ 80 - 15 = Q \]
\[ 65 = Q \]

Substitute \( Q = 65 \) back into the supply equation:
\[ P = 15 + 0.5(65) = 15 + 32.5 = 47.5 \]

New equilibrium price \( P = 47.5 \) and new equilibrium quantity \( Q = 65 \).

**5. Minh họa các kết quả trên cùng 1 đồ thị**

To illustrate the results on one graph:
- Plot the original demand \( P_D = 65 - 0.5Q \) and supply \( P_S = 15 + 0.5Q \) curves.
- Indicate the original equilibrium point (P = 40, Q = 50).
- Show the new equilibrium points for questions 2, 3, and 4 on the same graph.
- Include the new supply and demand curves as necessary.

Would you like a detailed graph for illustration, or do you have any specific questions on these calculations?

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Here are 5 questions you might ask next:
1. How do we derive the equilibrium condition in market models?
2. What is the economic significance of consumer and producer surplus?
3. How do taxes affect supply and demand curves?
4. Can you explain the concept of price elasticity in this context?
5. What happens if the government sets a price below equilibrium?

**Tip:** Always double-check calculations and ensure units and signs are consistent throughout economic analysis.

Explore detailed solutions to economic equilibrium problems involving consumer surplus, producer surplus, and changes in supply and demand. Learn how equilibrium price and quantity are determined using demand and supply equations. Suitable for advanced economics students and enthusiasts.

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